BOSTON – With their session expected to end Tuesday, Massachusetts lawmakers are running out of time to reconcile differences between House and Senate versions of a high-profile bill that targets spiraling health care costs.

Sen. Bruce Tarr, who serves on the committee charged with reconciling the two bills, said Wednesday he expects a compromise bill to be released early next week. The Republican from Gloucester expressed concerns the committee could finish its work in time for House and Senate members to review and vote on the legislation.

“I am somewhat disappointed that we’re in a situation where this is happening in the 11th hour because of the magnitude and the impact it will have,” he said.

The bill aims to lower health care costs in Massachusetts that came in the wake of landmark legislation signed in 2006 by then-Gov. Mitt Romney. The law expanded access to health coverage in the state, but premiums and other health care costs have threatened to undermine its long-term fiscal stability.

Gov. Deval Patrick told reporters Tuesday that he does not expect perfect legislation to come out of the committee, but believes they will create a “good bill.”

Earlier this session, the House of Representatives and the Senate each approved measures to contain health care costs before passing the bills on to a bipartisan panel of lawmakers. Both bills are aimed at saving the state billions of dollars over a 15-year period.

The House proposal includes a so-called “luxury tax” for hospitals that charge more than 20 percent above the state median price for a service. The hospitals would be levied a 10 percent surcharge that would go into a fund to help support hospitals serving the poor and most vulnerable.

Tarr said the surcharge is among the most significant differences between the two bills.

“There are a lot of issues where there is, in my opinion, a difference in philosophy between the House and the Senate and I would include that one in that category,” he said of the surcharge.

Tarr would not elaborate on discussion by the conference committee, which meets in private.

Conference committee chair Sen. Richard Moore declined to comment on the health care legislation. A spokesman for the Uxbridge Democrat said Moore was working to have a compromise bill to the Legislature before the end of the session.